Accelerated matrix recovery via random projection based on inexact augmented Lagrange multiplier method

作者：Wang Ping; Zhang Chuhan; Cai Sijia^*; Li Linhao

来源：Transactions of Tianjin University, 2013, 19(4): 293-299.

DOI：10.1007/s12209-013-2135-0

• Augmented lagrange multiplier methods
• Matrix completion
• Matrix recovery
• outlier pursuit
• Random projections
• Robust principal component analysis

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.

• 出版日期2013
• 单位天津大学